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arXiv · 2306.06248

A representation of sup-completion

Achintya Raya Polavarapu·Vladimir G. Troitsky
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Abstract

It was showed by Donner in 1982 that every order complete vector lattice $X$ may be embedded into a cone $X^s$, called the sup-completion of $X$. We show that if one represents the universal completion of $X$ as $C^\infty(K)$, then $X^s$ is the set of all continuous functions from $K$ to $[-\infty,\infty]$ that dominate some element of $X$. This provides a functional representation of $X^s$, as well as an easy alternative proof of its existence.

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Achintya Raya Polavarapu, Vladimir G. Troitsky. 2023-06-09. A representation of sup-completion. https://arxiv.org/abs/2306.06248

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